We report the adoption and invitation conversion probabilities w.r.t each measure in Figure REF  and Figure REF , respectively. We can find an evident correlation between each behavior and each proposed measure except for \({\mathsf {GS}}\) .
In terms of \(\#\)\({\mathsf {CC}}\) , contradicting the well-accepted insight of structural diversity [1]}, [2]}, [3]}, Figures REF (a) and  REF (a) show that the target user with less number of candidate groups (i.e., a less diverse neighborhood) is more likely to be invited and further adopt this invitation. Recently, this phenomenon also emerged from other user behaviors, especially in Tencent instant messaging platform [4]}, [5]}, but the underlying reason is still unclear. In contrast, \({\mathsf {SIT}}\)  can explain this as that a greater multi-membership makes the social identification phase of a target challenging due to the potential role conflict [6]}.
Regarding the effect of group size, we can find in Figures REF (b) and  REF (b) that the engagement willingness of users will be facilitated as the group scale increases, but subsequently hurdled if still going up. Notice that the source-target pair inside a medium-size group (i.e., level 3) is more likely to send an invitation and respond.
